Remark 4 Notice that the convergence-time to the consensus state is a function of the algebraic connectivity of the network [1]}, [2]}. Hence, to compute the gain \(\kappa \)  to obtain predefined-time convergence, we assume knowledge of a lower-bound of the algebraic connectivity of the network. For static networks, there exist several algorithms for distributively estimating the algebraic connectivity [3]}, [4]}, [5]}. For instance, the algorithm proposed in [4]} provides an asymptotic estimation, which is always a lower bound of the true algebraic connectivity. Another scenario is, given an estimate of the size of the network [7]}, [8]} to consider a worst-case \(\lambda _2\)  from information specific to the problem.

